Registered BAS agents (Bookkeepers) are entitled to charge you a fee for preparing activity statements if they are registered as a BAS agent with the Tax Practitioner Board (TPB).
Non registered bookkeepers cannot charge for Any services provided.
If the bookkeeper is an employee they may do this work for you and do not need to be registered.

BAS agents provide advice and services on the following tax and super issues:

GST

fuel tax

luxury car tax

wine equalisation tax

fringe benefits tax (collection and recovery only)

pay as you go (PAYG) withholding

PAYG instalments.

Agents must follow strict regulations that ensure they act in a professional manner.

Regardless of who records and reports information, you are still legally responsible for the accuracy of the information.